91Ó°ÊÓ

Area of an Ellipse. The area \(A\) bounded by an ellipse with the equation \(\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1\) is given by \(A=\pi a b .\) Find the area bounded by the ellipse described by \(9 x^{2}+16 y^{2}=144\)

Write each equation in standard form, if it is not alreacty so, and graph it. If the graph is a circle, give the coordinates of its center and its radius. If the graph is a parabola, give the coordinates of its vertex. $$ (x-2)^{2}+y^{2}=25 $$

Solve each system of equations for real values of x and y. $$ \left\\{\begin{array}{l} x^{2}=4-y \\ y=x^{2}+2 \end{array}\right. $$

Write each equation in standard form, if it is not alreacty so, and graph it. If the graph is a circle, give the coordinates of its center and its radius. If the graph is a parabola, give the coordinates of its vertex. $$ x^{2}+(y-3)^{2}=25 $$

Solve each system of equations for real values of x and y. $$ \left\\{\begin{array}{l} 3 x+2 y=10 \\ y=x^{2}-5 \end{array}\right. $$

A new subdivision of homes is planned for an area that military jets often fly over. On the coordinate system shown below, a sonic boom is heard by those on the ground within one branch of the hyperbola \(y^{2}-x^{2}=25 .\) How wide is the hyperbola 5 miles from its vertex?

Solve each system of equations for real values of x and y. $$ \left\\{\begin{array}{l} x^{2}-y^{2}=4 \\ x+y=4 \end{array}\right. $$

Write each equation in standard form, if it is not alreacty so, and graph it. If the graph is a circle, give the coordinates of its center and its radius. If the graph is a parabola, give the coordinates of its vertex. $$ x^{2}+y^{2}-6 x+8 y+18=0 $$

Explain the difference between the focus of an ellipse and the vertex of an ellipse.

Solve each system of equations for real values of x and y. $$ \left\\{\begin{array}{l} x-y=-1 \\ y^{2}-4 x=0 \end{array}\right. $$